Assignment-4-3502-S10 - STAT 3502 Assignment # 4 Total...

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STAT 3502 Assignment # 4 Total mark=25 Due: 9 August, 2010 prior to the start of class 1. Suppose that a random sample of size n is drawn from the Bernoulli distribution f ( x ; p ) = ( p x (1 - p ) 1 - x x = 0 , 1 0 otherwise. Find a maximum likelihood estimator of p .[3] 2. In a survey of 4720 American, 708 of them were overweight. calculate and interpret a 99% confidence interval for the proportion of all American who are overweight.[3] 3. For a sample of 69 healthy trees, the sample mean of dye-layer density was 1.028 and the sample standard deviation was 0.163. a. Calculate a 95% CI for the true average dye-layer density for all such trees.[2] b. Suppose the investigators had made a rough guess of 0.16 for the value of σ before collecting data. What sample size would be necessary to obtain an interval width of 0.05 for a confidence level of 95%?[2] 4. Consider a random sample X 1 , ··· ,X n from a pdf f ( x ; θ ) = 0 . 5(1 + θx ) - 1 x 1 , - 1 θ 1 show that ˆ θ = 3
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Assignment-4-3502-S10 - STAT 3502 Assignment # 4 Total...

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